X can complete 20% of the work in 8 days.

Therefore, 100% of the work will take: $8 \div 0.2 = 40$ days. Y can complete 25% of the work in 6 days.

Therefore, 100% of the work will take: $6 \div 0.25 = 24$ days. Work done together in 1 day:

Finding LCM of 40 and 24 = 120.

So, X and Y together can complete the entire work in 15 days.

Time required to complete 40% of the work: $40\% \times 15 = 6$days